(D) In steady state,the volume flow rate of water entering the vessel must be equal to the volume flow rate of water leaving the vessel through the ho

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(D) In steady state,the volume flow rate of water entering the vessel must be equal to the volume flow rate of water leaving the vessel through the hole.Let $Q$ be the rate of inflow,$a$ be the area of the hole,and $h$ be the height of the water level.The rate of outflow is given by Torricelli's law: $Q_{out} = a v = a \sqrt{2gh}$.Equating inflow and outflow: $Q = a \sqrt{2gh}$.Rearranging for $h$: $h = \frac{Q^2}{2 g a^2}$.Given $Q = 100 \ cm^3 s^{-1}$,$a = 1 \ cm^2$,and $g = 1000 \ cm s^{-2}$.Substituting the values: $h = \frac{(100)^2}{2 \times 1000 \times (1)^2} = \frac{10000}{2000} = 5 \ cm$.

Class 11 Physics Fluid Mechanics and Surface Tension Velocity of Efflux and Torricelli's law

Medium

$A$ cylindrical vessel open at the top is $20 \ cm$ high and $10 \ cm$ in diameter. $A$ circular hole whose cross-sectional area is $1 \ cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of $100 \ cm^3 s^{-1}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g = 1000 \ cm s^{-2}$)

A
$20$
B
$15$
C
$10$
D
$5$

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Fluid Mechanics and Surface Tension

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Velocity of Efflux and Torricelli's law

$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to zero is

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MediumAP EAMCET 2017

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If a small orifice is made at a height of $0.25\, m$ from the ground in a tank filled with water up to a height of $1\, m$,the horizontal range of the water stream will be (in $cm$):

DifficultAIIMS 2019

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$A$ large tank filled with water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from $h$ to $h/2$ and from $h/2$ to zero is

$A$ cylindrical container containing water has a small hole at a height of $H = 8 \text{ cm}$ from the bottom and at a depth of $h = 2 \text{ cm}$ from the top surface of the liquid. The horizontal distance (range) travelled by the water before it hits the ground is:

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